9/27/2010
C.L.(Chae Young Lim) Big idea: obeservation and description of changes in the world around us are the first steps in finding and learning about patterns.
Essential Question: How can I use graphs, tables and symbols to solve problems?
Notes From Class: Rate=ex.55miles per hour=one measured/another measurment
D=55T D=distance T=Time 4.2 Changing Speeds Problem 4.2
A. Make tables of time and distance data similar to the table you made for Problem 4.1, for travel at 50miles per hour and 65miles per hour. Plot the data from both tables on one coordinate grid. Use a different color for each set of data. Using a third color, add data points fir the times and distances traveled at 55 miles per hour (from Problem 4.1) ANS.
Time (hours)
Distance (miles)
0
0
1
50
2
100
3
150
4
200
5
250
6
300
7
350
8
400
Table for distance travelled at 50miles per hour
Time (hours)
Distance (miles)
0
0
1
65
2
130
3
195
4
260
5
315
6
380
7
445
8
510
Table for distance travelled at 65miles per hour
B. How are the tables for the three speeds similar? How are they different?ANS. They are similar because they are all increasing. They are different because the number by each distance is increasing different according to its speed. C. How are the graphs for the three speeds similar? How are they different? ANS. They are similar because all the graphs are moving upward. They are different because their gredient is different.
D. 1. Look at the table and graph for 65miles per hour. What pattern of change in the data helps you calculate the distance for any given time? In words, write a rule that explains how to calculate the distance traveled for any given time. ANS. Judging from table, it is clear that if we multiply the time by 65, we can get any require distance. 2. Use symbols to write your rule as an equation. ANS. 65t=d t=time d=distance E. 1. Now write a rule, in words, that explains how to calculate the distance traveled for any given time when the speed is 50miles per hour. ANS.Judging from table, it is clear that if we multiply the time by 50, we get any require distance. 2. Use symbols to write your rule as an equation. ANS. 50t=d t=time d=distance
F. How are the rules for calculating distance for the three speeds similar? How are they different? ANS. They are similar because they are all following same fomula(s*t=d). They are different because they have different numbers for speed.
Problem 4.2 Follow-up
1. After arrving in Philadelphia, Malcolm took the interstate home. He wrote the equation d=60t to represent his trip home. Explain this equation in words. ANS. d=60t means distance equals 60 multiply by the time they traveled.
2. How long would it take to reach Philadelphia-310miles from Williamsburg-travelling at 50miles per hour? 60miles per hour? 65miles per hour? ANS. 50miles per hour → 6 hours 12 minutes 60miles per hour → 5 hours 10 minutes 65miles per hour → 11 and 12/13 hours
C.L.(Chae Young Lim)
Big idea:
obeservation and description of changes in the world around us are the first steps in finding and learning about patterns.
Essential Question:
How can I use graphs, tables and symbols to solve problems?
Notes From Class:
Rate=ex.55miles per hour=one measured/another measurment
D=55T
D=distance T=Time
4.2 Changing Speeds
Problem 4.2
A. Make tables of time and distance data similar to the table you made for Problem 4.1, for travel at 50miles per hour and 65miles per hour.
Plot the data from both tables on one coordinate grid. Use a different color for each set of data. Using a third color, add data points fir the times and distances traveled at 55 miles per hour (from Problem 4.1)
ANS.
(hours)
(miles)
(hours)
(miles)
B. How are the tables for the three speeds similar? How are they different?ANS. They are similar because they are all increasing. They are different because the number by each distance is increasing different according to its speed.
C. How are the graphs for the three speeds similar? How are they different?
ANS. They are similar because all the graphs are moving upward. They are different because their gredient is different.
D. 1. Look at the table and graph for 65miles per hour. What pattern of change in the data helps you calculate the distance for any given time? In words, write a rule that explains how to calculate the distance traveled for any given time.
ANS. Judging from table, it is clear that if we multiply the time by 65, we can get any require distance.
2. Use symbols to write your rule as an equation.
ANS. 65t=d
t=time d=distance
E. 1. Now write a rule, in words, that explains how to calculate the distance traveled for any given time when the speed is 50miles per hour.
ANS.Judging from table, it is clear that if we multiply the time by 50, we get any require distance.
2. Use symbols to write your rule as an equation.
ANS. 50t=d
t=time d=distance
F. How are the rules for calculating distance for the three speeds similar? How are they different?
ANS. They are similar because they are all following same fomula(s*t=d). They are different because they have different numbers for speed.
Problem 4.2 Follow-up
1. After arrving in Philadelphia, Malcolm took the interstate home. He wrote the equation d=60t to represent his trip home. Explain this equation in words.
ANS. d=60t means distance equals 60 multiply by the time they traveled.
2. How long would it take to reach Philadelphia-310miles from Williamsburg-travelling at 50miles per hour? 60miles per hour? 65miles per hour?
ANS. 50miles per hour → 6 hours 12 minutes
60miles per hour → 5 hours 10 minutes
65miles per hour → 11 and 12/13 hours